I have a very simple question about polar coordinate system. According to Wikipedia, the angle is defined as:
where atan2(y,x) is defined as "a common variation on the arctangent function"
Since I'm not an advanced student in calculus, I was trying to determine these values as an exercise, just by appling the inverse relation between tangent and arctangent function, and by noticing that the ratio of the argument of the arctangent function is in fact the ratio between the sinus and the cosinus of the angle. I've found correctly the values for the angle in the last three cases of the system above, but I don't understand why I should add and subtract \pi in the second and third case respectively. Isn't the period of the tangent function equal to \pi itself? Why am I wrong? I suppose that there is some advanced additional stuff that I can't understand! As usual, thank you!